Landform Characterization with
Geographic Information Systems
Jacek S. BI
Abstract
The ability to analyze and quantify morphology of the surface of the Earth in terms of landform characteristics i s essential for understanding of the physical, chemical, and
biological processes that occur within the landscape. However, because of the complexity of taxonomic schema for
landforms which include their provenance, composition, and
function, these features are difficult to map and quantify using automated methods. The author suggests geographic information systems (GIS) based methods for mapping and
classification of the landscape suqface into what can be understood as fourth-order-of-relief features and include convex
areas and their crests, concave areas and their troughs, open
concavities and enclosed basins, and horizontal and sloping
flats. The features can then be analyzed statistically, aggregated into higher-order-of-relief forms, and correlated with
other aspects of the environment to aid fuller classification
of landforms.
Introduction
The ability to analyze and quantify morphology of the surface of the Earth is essential for understanding the physical,
chemical, and biological processes that occur within the
landscape. The shape of terrain influences flow of surface
water, transport of sediment and pollutants, climate both on
local and regional scales, nature and distribution of habitats
for plant and animal species, and migration patterns of many
animal species. It is also an expression of geologic and
weathering processes that have contributed to its formation.
Knowledge of terrain morphology also is essential for any
engineering or land-management endeavors that affect or disturb the surface of the land.
The primary science that deals with understanding, description, and mapping of the shape of terrain is geomorphology, defined in the Random House Webster's Dictionary
as the study of the characteristics, origin, and development
of the form or surface features of the Earth, i.e., landforms.
Landforms are defined as specific geomorphic features on the
surface of the Earth, ranging from large-scale features such as
plains and mountain ranges to minor features such as individual hills and valleys. Geomorphology encompasses a
spectrum of approaches to the study of landforms within two
major interrelated conceptual frameworks: functional and
historical. The functional approach tries to explain the existence of a landform in terms of the circumstances which surround it and allow it to be produced, sustained, or transformed such that the landform functions in a manner which
reflects these circumstances, while the historical approach
tries to explain the existing landform assemblage as a mixture of effects resulting from the vicissitudes through which
it has passed (Chorley et al., 1985). Taxonomic schemes for
National Applied Resource Sciences Center, Bureau of Land
Management, Denver Federal Center, Bldg. 50, P.O. Box
25047, Lakewood, CO 80225-0047.
PE&RS
February 1997
landforms therefore often include the way they were formed,
their composition, and the environment in which they were
formed.
The ability to map landforms is an important aspect of
any environmental or resource analysis and modeling effort.
Traditionally, mapping of the aspects of the environment has
been accomplished through in situ surveys. The advent of
aerial photography and satellite remote sensing have made
surveys of large areas easier to accomplish, although this
technology still requires in situ verification and ground-truthing. While remote sensing technology can provide tremendous amounts of information about the surface of the Earth, it
is incapable of providing all of the data needed. The most
complete approach to mapping the distribution of various environmental parameters requires an integrated approach that
relies on remote sensing and geographically referenced field
survey data, whether in cartographic or tabular format. By
combining mapped data hom various sources, it is often possible to make informed guesses about those characteristics of
the environment that remain hidden to satellite sensors or aerial cameras. For example, through correlation of mapped information on vegetation types with data on local climate,
topography, hydrology, geology, and general distribution of
soils and through application of the knowledge of surface processes that relate to soil formation, detachment, and transport,
it is possible to make relatively accurate predictions regarding
distribution of different types of soils, something not currently
possible using remote sensing data alone.
Traditionally, these types of studies have been performed
using a manual overlay process that relies on maps hand-drawn
on transparent velum. Currently, geographic information systems (GIS) permit integration of geographic data using computers. Surveyed information is entered into a GIs and presenred in
digital format, where it can be combined with remote sensing
images to generate new maps using various automated spatial
data processing algorithms. The knowledge-based process that
combines existing geographic data to generate new information
is generally known as cartographic modeling. The component
maps that show the geographic distribution of a single environmental parameter or a single category of parameters are known
as geographic themes.
When a theme represents a category of information that
consists of many data elements, it is possible to generate
new maps from a single geographic theme by selectively displaying the elements. For example, a single soil mapping
unit within a soils theme can have numerous attributes associated with it, such as data on the organic matter content, pH
factor, salt content, percentages of silt and clay, erodibility,
structure, and other information. Using a GIS, each kind of
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Photogrammetric Engineering & Remote Sensing,
Vol. 63, No. 2, February 1997, pp. 183-191.
0099-1112/97/6302-183$3.00/0
O 1997 American Society for Photogrammetry
and Remote Sensing
information can be selectively identified, displayed, and
saved as an independent data layer for use within a cartographic model.
In the above example, a GIS functions mainly as a display or selection device for various soil attributes already
known. However, a GIS also permits automated extraction of
completely new information from an existing theme. This is
particularly the case with topographic data traditionally
available as elevation contour maps. From the contour map
various types of information, such as watershed boundaries,
steepest flow paths, slope gradients, slope aspects, and more,
can be derived by a specialist through painstaking manual
analysis of the shape of the contours and the distances between contour lines.
In digital format, elevation data are generally available
as grids, where each grid cell represents a particular elevation above a certain vertical reference, such as the mean sea
level. Geographic information systems include various algorithms that mathematically analyze the digital elevation data
to automatically derive information that otherwise would
take tremendous effort and amount of time to obtain. Typical
terrain analysis algorithms in a GIs include methods for generating slope gradients, slope aspects, watershed boundaries,
and flow paths. The added bonus of using these automated
means is that new information is always calculated in precisely the same way, eliminating subjective judgement on the
part of the analyst.
Automated extraction of new information from digital elevation models (DEMS) has many levels of complexity. Generation of slope and aspect maps is a relatively simple process,
while delineation of watershed boundaries or steepest flow
paths requires more complex calculations. Yet another level
of complexity is reached when topographic parameters for
physical processes are very closely associated with other
parameters not directly related to elevations. For example,
while movement of sediment across terrain is strongly dependent on topography, other factors such as the amount
vegetation cover, type of soils, and intensity of rainfall govern sediment transport and interact in complex ways with
the topographic factors. Analysis of elevation data to provide
useful information for sediment transport modeling therefore
requires a precise understanding of the contribution of topography to the movement of soils and an analysis of that contribution in isolation from other factors that influence
movement of sediment across the landscape. Currently,
much research is being performed to develop new terrain
analysis algorithms to model such processes (Beven and
Moore, 1993).
A similar issue arises in classification of landforms, although here it is mostly a question of definition and taxonomy. What do we understand a landform to be? To what
extent can we think of landforms purely in terms of shapes
in isolation from questions concerning their origin and composition? If so, is there a simple way to determine the shapes
of landforms from elevation data?
This paper proposes a simple approach, based mostly on
existing GIS capabilities, to extract meaningful information
from digital elevation data that can ultimately lead to precise
mapping of landforms independently of taxonomic schemes.
While the methods described here cannot provide instant
identification of the nature, probable origin, or composition
of any particular landform, the information generated
through them can be used as part of a more complex cartographic modeling process that will potentially accomplish
that goal.
Classification of Landforms for GIS Processing
More specific definitions of the term landform than those
quoted previously come from Belcher (1948) and Lueder
(1959). According to Belcher, each landform presents separate and distinct soil characteristics, topography, rock materials, and groundwater conditions. He adds that the recurrence
of the landform, regardless of the location, implies a recurrence of the basic characteristics of that landform (Belcher,
1948). Lueder, on the other hand, describes a unit landform
as a terrain feature or terrain habit, usually of the third order, created by natural processes in such a way that it may
be described and recognized in terms of typical features
wherever it may occur, and which, when identified, provides
dependable information concerning its own structure and either composition and texture or uniformity (Lueder, 1959). In
identifying landforms as the third-order-of-relief features,
Lueder narrows the definition down by placing landforms
more in the context of shape of the land, and within the traditional orders-of-relief framework. In that framework, the
first-order-of-relief is represented by continents and ocean
basins; the second order by mountain ranges, plains, continental shelf, continental rise, and the abyssal plains; while
the third order by the landscape features such as individual
hills, mountains, and valleys. Of course, for the purposes of
precise mapping, the question still remains, where to place
the boundaries of features.
Lueder's definition serves as a departure point for analysis of landform characteristics based purely on elevation
data. While it is unclear whether identification of the thirdorder-of-relief features will provide dependable information
concerning the landform's own structure, composition, or
texture, elevation data implicitly contains information on the
shape, vertical order, and magnitude of relief features. However, because of problems with definition, it is very difficult
to agree on the precise boundaries of third-order-of-relief features. It is much easier to identify and delineate portions of
these features as related to the fact that they represent a part
of a continuous surface. Each complex continuous surface
can be said to consist of concave areas, convex areas, and
flats. Convex areas can be further subdivided into crests and
sideslopes. Concave areas can be subdivided into troughs,
sideslopes, and open and enclosed basins. Flats can be divided into sloping flats and horizontal flats. In the context of
terrain analysis, these subfeatures can be referred to as the
fourth-order-of-relief features. Most or all of the fourth-orderof-relief features are always present in any terrain, and a
digital surface representation of the terrain can be analyzed
to identify discrete boundaries for these categories. The features can then be aggregated to form higher-order-of-relief
categories using diverse definitions or taxonomic schema and
multi-thematic support data.
Landform characterization maps where the continuous
terrain surface is classified into fourth-order-of-relief features
provide information on the shape, vertical order, and magnitude of the features. Shape refers to the two-dimensional and
three-dimensional distribution pattern of any particular feature. Vertical order refers to the fact that, within its immediate neighborhood, a crest is the highest area on a convexity
(e.g., a hill), a convexity is higher than a concavity, and a
trough is the lowest area within a concavity (e.g., a depression). Magnitude refers to the actual elevations of the features, and the fact that some hills are higher than others and
some depressions are deeper than others. Magnitude also includes any other characteristic that can be derived from elevation values for any particular feature, such as the average
slope gradient of a crest or the areal extent and volume of an
enclosed basin.
Analysis for Convexity, Concavity, and Flatness
Qualities of concavity and convexity are synonymous with
whether a particular neighborhood or area on the surface of
the Earth predominantly tends toward being a depression or
February 1997 PE&RS
a protrusion. Curvature is generally understood as a directional property. Some existing G I systems
~
offer methods to
determine profile curvature, or curvature of a surface in the
direction of slope, and planform curvature, or curvature of a
surface perpendicular to the direction of slope, examplified
by algorithms based on the work of Moore et al. (1991) and
Zeverbergen and Thorne (1987). However, after several attempts to use these, the author found them to be insufficient
for his purposes and it therefore became imperative to develop a different method. This method, although quite simple, is currently (to the best knowledge of the author) not
available in any of the existing geographic information systems and has not been previously discussed in the literature.
However, the method should be easy to program by those
who are interested in using it.
The new approach is a modification of an existing
method for calculation of the average percent slope gradient
for a center cell within a neighborhood (matrix) the size of
which is specified by the user. The existing algorithm calculates the values of the slopes between the center cell and
neighborhood cells by taking the absolute value of the difference in elevations between the center cell and other cells in
the neighborhood (rise) and dividing it by the horizontal distance between them calculated using the Pythagoranean theorem (run). It then takes the average of the positive fractional
value thus obtained and multiplies it by 100 to derive a percent slope gradient value that is assigned to the central cell
of the neighborhood. The entire grid is processed in that way
by proceeding to the next cell in a row (line) and repeating
the same procedure, and then moving to the next row in the
elevation grid until the entire grid is processed.
To obtain information as to whether the center cell of a 3by 3-cell neighborhood is part of a convexity, a concavity, or a
flat, the average percent slope gradient algorithm was modified by the author in a simple way. The first step of this modification was to ensure that the calculation of the rise occurs
through subtraction of the elevation value of the neighborhood
cell from the elevation value of the center cell. The second
step was to eliminate the absolute value function from the
"rise" calculation, which resulted in either positive, negative,
or zero values for the rise and therefore for the slope. Negative
rise values indicate that the neighborhood cell lies above the
center cell, positive values that the neighborhood cell lies below the center cell, while a zero value indicates equal elevations. Summation and averaging of these values results in a
negative, a positive, or a zero value being assigned to the center cell. Positive values mean that the central cell is within a
3- by 3-cell neighborhood that has a predominantly convex
shape, while negative values indicate a predominantly concave shape of the surface. Zero values indicate either a flat or
an area where convex and concave curvatures cancel each
other out, such as a saddlepoint. The method seems to work
well in identifying convexities, concavities, and flats.
The method is partially based on the nine basic geometric forms of hillslopes (Chorley et a]., 1985) with each form
represented using a 3- by 3-cell grid. Figure 1 shows some of
the representative combinations of elevation values within
the neighborhood. A graph is included with each example to
show the relative impact of the positive and negative slopes
calculated on the value of the center cell. The y-axis shows
the elevation differences in the positive or negative directions, while the x-axis shows the positive distance from the
center cell to any of the neighborhood cells. Because the
magnitude of 1 is used for the width and height of the cells,
the horizontal distance from the center cell to any of the adjacent cells is either 1 or (using the Pythagoranean theorem)
the square root of 2, which is approximately 1.41. A line is
extended from the center cell (the origin on the graph) to a
point on the graph that represents the location of the neighPE&RS
February 1997
borhood cell. The slope of the line is the slope gradient between the center and neighborhood cell. Each line is marked
with a number ranging from 1 through 8, which represents to
which of the neighborhood cells the line connects.
The graph is a visual way of showing how negative or
positive slope gradient values within the matrix are used to
evaluate whether the center cell lies within a generally convex, concave, or flat neighborhood. The algorithm calculates
positive, zero, or negative slopes and then averages the values, assigning the result to the center cell. This is equivalent
to adding all the slopes derived from the graph and dividing
them by the number of neighbor cells, which in this example
is equal to eight. If the elevation differences and slopes
shown on the graph are predominantly negative both in magnitude and number, the center cell lies in a neighborhood
that is generally concave; if positive, then it lies in a generally convex neighborhood. When the positive and negative
elevation differences and slope magnitudes cancel each other
out, the area is either flat, or represents equal amounts of
convexity and concavity which cancel each other out. An example of the latter, as already mentioned, can be a saddlepoint, or an inflection point where the curvature of the slope
changes from concave to convex.
Comparison of the shaded map that resulted from processing of a DEM using this algorithm, with its portrayal of
convex, concave, and flat areas, to the contour map and the
shape of the contours within any particular neighborhood,
indicates that the method is accurate to the degree that the
data are accurate. An example is provided in Figure 2, which
shows convex, concave, and flat areas with elevation contours overlaid on top for a portion of the USGS 7.5-minute
Sagebrush Hill quadrangle in Colorado.
The size of the neighborhood used for the analysis can
currently be varied by the user from 3 by 3 cells to 31 by 31
cells. In a USGS 7.5-minute DEM with 30- by 30-m cell size,
this means that in the first case positive, negative, and zero
slopes are averaged over an area of 90m by 90% while in the
latter case over an area of 930m by 930m. In the h s t case this
means that the longest horizontal distance (run) from the center cell to a neighborhood cell is 42.426 m, while in the latter
case it is 636.396 m. The upper limit of 31 by 31 cells is not
fixed and represents an arbitrary cutoff point.
For a neighborhood of any size within the current limits,
the algorithm calculates slopes by directly evaluating the rise
and run from the center cell to each of the neighborhood
cells. The longer the run, the smaller the slope gradient
value. Therefore, the value assigned to the center cell is a
distance weighted average of all the slopes possible within a
given neighborhood. For a 31- by 31-cell neighborhood using
a 30-m by 30-m DEM, this means that 960 slope calculations
are performed for cells as close as 30 m or as far as 636 m
away, and the classification of a given cell as convex, concave, or flat is influenced by distant elevation values. This
has the effect of generalizing or smoothing of information on
trends in curvature of the landscape. For a 31- by 31-cell
neighborhood, only if the entire 864,900-mZarea considered
by the algorithm exhibits average positive slopes can the
center cell of that area be considered convex. Figure 3 shows
the generalized convexities, concavities, and flats for the
same area as Figure 2. Instead of highly bagmented mosaic,
only the large trends in land curvature, such as ridge formations and valleys, are re~resentedon the map. The flat areas
appear mostly at the boAdary between the generally convex
and concave areas. indicatine locations of inflection where
the total weight of positive A d negative slopes is in balance.
Further Classification of Digital Terrain Data
Additional information about the terrain can be extracted
from DEMs using the surface hydrologic terrain analysis capa-
Elevation
difference
8
'
7
2
Average slope = -0.60
2
3
Distance from
Centercell
6
5
-1
(2 4, 6 ,
I
-2
The elevation differences and the slopes from
the center cell to neighborhood cells are negative
or equal to zero, therefore the center cell lies in
a 3x3 cell neighborhood which is generally
concave.
Elevation
diierence
8
'
2
Distance from
center cell
6
5
-1
Elevation
difference
Average slope = 0.30
7 4 3 1
4 3 1
5
Distance from
center cell
.41
(6.8)
-1
-2
-1
Elevation
dinerence
2 1
The elevation differences and the slopes from
the center cell to neighborhood cells are positive
or equal to zero, therefore the center cell lies in
a 3x3 cell neighborhood which is generally
convex.
(7)
Although the elevation differencesand slopes from
the center to neighborhood cells 7,6, and 8 are negative, the elevation differences and slopes to cells
2, 3, and 4 are positive and greater in magnitude.
Since the flat slopes have no influence, the center
cell lies in a 3x3 cell neighborhood which is generally convex.
Average slope = -0.30
0
1.41
Distance from
center cell
-1
(6.8)
-2
Although the elevation differences and slopes from
the center to neighborhood cells 2,3 and 4 are positive, the elevation differences and slopes to cells
7,6, and 8 are negative and greater in magnitude.
since the flat slopes have no influence, the center
cell lies in a 3x3 cell neighborhood which is
generally concave.
(7)
Elevation
dilference
2
Average slope = 0
Distance from
Centercell
-1
(4.8)
Since the elevation differences and slopes cancel
each other out, the value assigned to the center
is zero despite the fact that the neighborhood is
not genuinely flat. This situation is similar to
a "saddlepoint" in nature where the convex
and concave curvatures cancel each other out.
Figure 1.A graph depicting five different combinations of elevation values within a 3- by 3-cell neighborhood and vectors representing negative, positive, and zero value slopes between the center and neighborhood cells.
bilities developed by Jenson and Domingue (1988). The software was originally designed to delineate catchments and
flow paths from digital elevation data.
As one of the first steps of processing to delineate catchments (watersheds), Jenson's software provides an algorithm
for filling single-celled and multi-celled depressions in digital elevation models. This is important because, to calculate
watershed boundaries, it is necessary to route the flow of water across the entire DEM, and therefore across surface depressions. Because most single-celled depressions in DEMs
are a product of errors in generation of the models, the
multi-celled depressions are of greater interest because they
are more likely to represent actually existing enclosed basins
on the surface of the Earth.
February 1997 PE&RS
cells on opposite sides have an equal drop, then one of them
is arbitrarily chosen.
In the fourth condition, the center cell is located in a flat
area and all cells are equal (or greater) in elevation. The outflow point is not known. First, to determine flow direction,
all of the cells belonging to the first, second, or third condition are resolved. Then, in an iterative process, cells are assigned to flow toward a neighbor if the neighbor has a
defined flow direction that does not point back to the tested
cell. In this way, the flow direction assignments grow into
the flat area from the flat's outflow point until all of the cells
have flow directions assigned.
From the flow direction map, it becomes possible to calculate flow accumulation for each cell. The flow accumulation map contains, for each of its cells, an integer value that
represents how many other cells are "flowing" into any particular cell along steepest pathways. Because generation of a
flow direction map from a filled DEM establishes paths across
depressed and flat areas of the landscape, the cells having
the flow accumulation value of zero (to which no other cells
flow) should correspond to the pattern of crests of ridges.
Another way to consider the crests is to realize that the zero
flow accumulation areas consist of those cells that represent
local elevation maxima (are at the top of a convexity), and
where the slope gradient between them is less than the slope
gradient between the cells in other portions of a convexity.
To put it in yet another way, water is modeled as flowing
away from the cells that represent a crest, because, in this
definition, the crest is constituted of cells that have less of an
elevation difference between themselves than there is between the cells of the crest and of the sideslopes.
How well will this definition hold for modeled landscapes and correspond to real landscapes? The best answer
is that the current definition of crests is only adequate. While
it applies in most cases, there are situations in which flow
will occur along the identified crest. Better methods to deal
with this problem will need to be developed in the future;
however, the current methods might be adequate for a variety of modeling efforts.
The cells with values greater than zero in the flow accumulation data set made from a filled DEM delineate a fully
-
Figure 2. Convex (horizontal lines), concave (unshaded),
and flat areas (dark shade) delineated using a 3- by 3cell matrix for a portion of the u s ~ s7.5-minute Sagebrush Hill quadrangle in Colorado. Streams and elevation
contours are also shown.
The algorithm for filling multi-celled depressions fills
them to their pour point. Imagine a tilted bowl that is being
filled with water. At some point in time, the water will start
flowing out of the bowl at its pour location, which is the
lowest point on the edge of the bowl. The area covered by
the surface of water in the bowl (basin) as the water begins
to flow out is equivalent to the areal extent of the enclosed
basin in map view. To obtain a map that shows the areal extent of enclosed basins, it is necessary to subtract the original
unfilled DEM from the filled DEM. Because the resultant digital map contains values that represent the depth of each basin, it is also easy to calculate the volume of each basin
using standard GIs techniques.
As the next step toward deriving watershed boundaries
from digital terrain data, Jenson's software contains algorithms to calculate flow directions from the filled DEM. The
flow direction for a cell is the direction water will flow out
of the cell along the steepest path. This is encoded in the
flow direction map as a value that represents the orientation
of flow toward one of the eight cells that surround it. The
flow direction algorithm resolves the problem of routing potential water flow through the landscape by providing solutions for four possible conditions that determine flow direction.
The first condition occurs only if the algorithm is used
on unfilled DEMS and will not be discussed here. (For a detailed discussion of these methods, see the original paper by
Jenson and Domingue (1988) or the HTAS User's Manual, prepared by the author in 1993 and listed in the references.)
The second condition occurs when the distance-weighted
drop from the central cell is higher for one of the surrounding cells than for the other neighborhood cells. A flow direction value is assigned to the central cell of a 3 by 3 matrix in
the direction of the cell where the drop (or the slope gradient) is the steepest.
In the third case, there are two or more cells that have
the same steepest drop, and one has to be selected as the direction of flow. This is accomplished using a logical table
look-up operation, where, for example, if three adjacent cells
have the same steepest drop from the center cell, the middle
one of these cells will be chosen for direction of flow. If two
PE&RS February 1997
-~~
Figure 3. Convex (horizontal lines), concave (unshaded),
and flat areas (dark shade) delineated using a 31- by 31cell matrix for a portion of the U S G ~7.5-minute Sagebrush Hill quadrangle in Colorado. Streams and elevation
contours are also shown.
187
connected drainage network. If one selects ranges of flow accumulation values for display, then as the lowest value in
this range is decreased, the density of the drainage network
displayed will increase. This is because a greater number of
smaller flow path tributaries are shown. Because the cells in
the flow path are in an ordered relationship to each other, so
that, in almost all cases, each consecutive cell has the lowest
elevation of all the cells surrounding the previous cell, these
flowpaths form a trough of a valley and represent a sequence
of lowest points within an open basin.
Within a closed basin (a surface depression), a trough is
essentially the point or points with lowest elevations within
the basin. Geographic information systems permit analysis of
groups of cells and extraction of statistical information about
them, such as the minimum and maximum elevation values.
Here, the minimum value in a group of cells that represents
an enclosed basin is considered to be the trough. Figure 4
shows crests, troughs of open basins, and closed basins for a
portion of the uSGS 7.5-minute Sagebrush Hill quadrangle in
Colorado.
Flats are extracted from the DEM using the curvature
analysis method described in the previous section; however,
this method does not provide a way to separate sloping from
horizontal flats. To do so, it is necessary to apply the unmodified average percent slope gradient algorithm to the DEM,
which results in a slope gradient map. Extraction of zero values from this map results in a map of horizontal flats that
can then be displayed separately from the other flats, i.e., the
ones that have a slope gradient greater than zero and are
therefore not horizontal.
Figure 5 shows a simplified three-dimensional view of
landform features draped over a portion of the digital elevation model for the USGS 7.5-minute Sagebrush Hill quadrangle in Colorado. Convexities and concavities in this
illustration were derived using a 31 by 31 neighborhood.
Potential Enhancements of the Landform Characterization
Method
The product of the procedures described in previous sections
is either a digital or a hardcopy map that separates the landscape into concave and convex areas, crests and troughs, enclosed basins, sloping flats, and horizontal flats. The digital
map of the features explicitly contains information on the
shape, and implicitly on the vertical order and magnitude, of
the features. Each discrete area has a specific shape in twodimensional map view and in three dimensions. Vertical order is implicit in the identification of each feature as being a
crest, a convexity, a concavity, or a trough. Within any particular local neighborhood, a crest is the highest area on a
convexity, a convexity is higher than a concavity, and a
trough is the lowest area of a concavity. The data on the
magnitude of each feature is implicitly contained in the location of each cell on the map. To obtain actual values, the
original DEM has to be available to serve as a reference data
layer. The values can either be displayed as contours, or interactively queried within a GIS.
Extraction of discrete entities from a continuous elevation data set opens up possibilities for further statistical analysis of the morphology of individual features in isolation
from other features. This can be accomplished by obtaining
statistical summaries for each feature or group of cells using
various GIs statistical operations. Such summaries can include, for example, the maximum, minimum, and average elevations, slope gradients, or slope aspects for any given area.
Other types of summaries are also possible. The statistical
data can then be placed as each feature's attribute in an attribute table.
One of the problems that might arise is that a particular
feature, such as a ridge, can extend continuously through a
large portion of the map to the point where statistical summaries became less meaningful. If that is the case, the map
can be edited further. In raster format, it can be combined
with an aspect map so as to separate the ridge into slopes
facing in opposite directions. In vector format, a feature can
be subdivided by placing or removing lines that represent
feature boundaries to create new, more specific features. Features can also be aggregated using similar methods.
This type of analysis, while requiring user interaction in
the edit stage, could be automated to the point that the statistics for each feature of the final product would be automatically displayed in a table format if the feature was
pointed and clicked at with a cursor. Such an automated
landform characterization system could become a module
within a geographic information system and could include
other methods of terrain analysis, e.g., methods for calculation of roughness factors, for fractal analysis, etc.
Once continuous terrain information is classified into
discrete entities, it also becomes possible to analyze the variety of these entities using commands such as FOCALVARIETY
or ZONALVARIETY available in ARCIINFO software. FOCALVARIETY analyzes the diversity of discrete features using a roving
window of size specified by the user. It assigns a value that
represents the number of distinct features found within a
neighborhood to the center cell, and therefore the values in
the resultant map indicate the variety of entities found
within a certain distance from any point on the landform
map. ZONALVARIETY works in a similar manner, except that
it identifies a variety of features for areas defined by the extent of some other environmental parameters, such as soil or
vegetation type. FOCALVARIETY can provide a way to compare various terrains by identifying diversity of features
found within a neighborhood of certain size. ZONALVARIETY
can be of help as a correlation device by providing a method
to identify diversity of features found within the boundaries
of unique mapping units that represent the spatial extent of
some aspect of the environment. Using this command, it
might be possible to correlate the diversity of landform features within a particular soil or vegetation type to the diversity found within other soil or vegetation types, or any other
discrete areas that represent the extent of some environmental parameter.
Possible Applications of Fractal Analysis with the Landform
Methods
The algorithm to determine convex, concave, and flat areas
allows for analysis of the influence of elevation values at various distances from the center cell through changing of the
size of the neighborhood used for calculations. Furthermore,
ARCIINFO software permits various shapes of neighborhoods,
including a wedge shaped windows oriented in directions
specified by the user, and neighborhoods where each of the
neighbor cells can be assigned some weighted factor value.
These capabilities permit a variety of approaches to generalization, and therefore to analysis of the relationships between
topographic trends and the shape of the fourth-order-of-relief
features.
The following discussion concerns possible benefits that
might be derived from analysis of terrain using a change in
the size of a square neighborhood surrounding the center
cell. A simple increase in the size of the window results in a
decrease in fragmentation of the features and in the sinuosity
of the boundaries of the features. Potentially in some landscapes this decrease is gradual, while in others there can be
a sudden lessening in fragmentation and sinuosity at some
threshold window size. The various patterns of these changes
occur in dependence on the trends in shape of the terrain,
and are presumably different for different landscapes.
One way to quantify the degree of fragmentation and
February 1997 PE&RS
landform feature fragmentation and shape. Figure 6 shows
the changes in fragmentation of the features and sinuosity of
the boundaries with changing window size for a portion of
the U S G ~7.5-minute Sagebrush Hill quadrangle in Colorado.
The next step would be to compare different types of
landscapes to see if their "signatures" are adequately different and distinct to be of use in classifying terrains into similar groups. If such a pattern does exist, landform methods
combined with fractal analysis can potentially be used to develop an index for various types of landscapes based on their
morphology. From this information conclusions could potentially be drawn with respect to the nature and the geographical extent of morphic patterns for different terrains and the
processes that have shaped them. Additionally, such an approach can provide a way to classify large areas into more
general categories of similar terrains than is possible with the
current methods.
Environmental and Resource Analysis Applications
Figure 4. Crests of convexities (crosshatch), troughs (diagonal lines), and enclosed basins (dark shade) delineated for a portion of the USGS 7.5-minute Sagebrush Hill
quadrangle in Colorado. Streams and elevation contours
are also shown.
sinuosity for each window size would be to measure their
fractal dimension. If the fractal dimensions show a clear and
narrow range of values for each neighborhood size for a particular type of terrain, these values can be plotted against the
window size. Such a graph could potentially reflect a unique
"signature" for the particular landscape studied. The "signature" would be an expression of the influence of the shape of
the landscape at various distances from the center cell on the
The landform characterization methodology described in this
paper is essentially a morphometric technique which permits
objective classification of any digital surface. It allows for
quick analysis of elevation data for vast tracks of land, eliminating the painstaking process of manual analysis of contoured representation of surfaces. In manual approaches the
difficulties involved in contour interpretation introduce a
level of subjective judgement that makes a precise comparison of various types of terrain from different locations difficult to accomplish. Because with automated methods terrain
data are always analyzed in precisely the same way, the only
source of error in such comparative studies arises kom the
difference in quality of digital elevation data from area to
area.
A clear use of landform characterization methods is
therefore a mapping tool which provides another way of representing terrain information that is complementary to con-
Concave areas
Convex areas
Troughs
r'-i;j\l
~~evations
contours
USGS DLG stream
Figure 5. A three-dimensionalview of a portion of the Sagebrush Hill quadrangle in Colorado with draped landform categories (generalized using a 31- by 31-cell neighborhood).
Streams and elevation contours are also shown.
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189
a. Convex, concave, and flat areas delineated
using a 3x3 cell neighborhood.
b. Convex, concave, and flat areas delineated
using a 7x7 cell neighborhood.
using a llxll cell neighborhood.
using a 19x19 cell neighborhood.
e. Convex, concave, and flat areas delineated
using a 25x25 cell neighborhood.
f. Convex, concave, and flat areas delineated
using a 31x31 cell neighborhood.
F~gure6. The effects of increasing the neighborhood size on fragmentation of features
and sinuosity of boundaries delineated for a portion of the usGs 7.5-minute Sagebrush
Hill quadrangle in Colorado.
touring. Because the tool classifies the continuous landscape
surface into meaningful fourth-order-of-relief categories represented by areas with discrete boundaries, the resultant map
permits aggregation of landform features into distinct geomorphological units. Each such unit can be developed to
represent a unique set of geomorphic controls on the ecosystem processes in the landscape. Furthermore, similar units
can be grouped together according to type so that large areas
of land are represented by several distinct groups of units.
Potentially, the results of intensive data collection, analysis,
and modeling of the influence of geomorphic controls on environmental processes and patterns performed in representative units could be extrapolated to other units within the
same group. This could lead to improved understanding of
the influence of terrain characteristics on ecosystem processes for large regions and for a variety of environments.
The classification of continuous terrain surface into discrete and meaningful categories can also be of aid in mathe-
matical analyses of terrain content and pattern of areas
identified according to taxonomic schemes based on other
aspects of the environment. For example, statistical summaries of landform feature content within a soil and vegetation
unit, and comparison of the summaries between the units,
may yield clear differences in feature distributions between
this or that soil or vegetation type. Such methods can be easily automated and can permit statistical correlation between
terrain morphology and other environmental parameters. Beyond that, fractal analysis of the shape of landform feature
boundaries can provide additional data for this type of correlation.
The techniques for analysis of feature content and pattern can also be applied to digital elevation data for the same
areas but at various resolutions and levels of detail. Comparison of the loss or increase in feature content and the difference or similarity in patterns with change in resolution
could potentially lead to developing a better understanding
February 1997 PE&RS
of scaling relationships in terrain data, and in identifying the
level of self-similarity for data at various scales. This approach could also be of benefit in quantifying sub-pixel microrelief for various types of landscapes.
Because the methods proposed here can provide an accurate description of the morphology of a three-dimensional
feature, they can potentially be used to model processes that
generated a particular feature. An example of such an approach can be provided in the context of the equilibrium
theory of coastal landforms. From Tanner (1974), "the equilibrium idea is that an energetic wave system will establish
in due time and barring too many complications, a delicately
adjusted balance among activity, three-dimensional geometry, and sediment transport such that the system will tend to
correct short or minor interference." To put it in another
way, the energy input from waves results in sediment transport processes which cause morphological change. That
change will continue indefinitely unless a landform is produced in which the energy is dissipated without any net sediment transport. Should the equilibrium concept be accurate
and applicable to a variety of coastal landforms, the landform analysis methods proposed here can provide quantitative information on the three-dimensional geometry aspect of
the equilibrium landform, potentially leading to development
of models that account for sediment transport processes that
determine its morphology in terms of the local wave energy
regimes.
Correlation and interpretation of terrain characteristics
with other data can permit detailed analysis of the interaction of landscape morphology with other aspects of the landscape. Interpretation of geologic and soil data in combination
with landform data can aid in understanding of the provenance of landforms and provide a more complete picture of
the geomorphology of an area. Landform maps can also provide one of the constituent data layers for soil survey enhancement and premapping prior to in situ soil survey
efforts. Correlation and interpretation of landform data with
vegetation, soil, climate, and geology data can lead to better
understanding of the influence of terrain characteristics on
vegetation distribution patterns in landscape ecological studies. Landform patterns can be useful in generating hydrologic
response unit (HRU) maps important in various hydrologic
models. The shape of terrain is also of relevance for habitat
studies. Similar approaches can be utilized in studies of submarine geomorphology and distribution patterns of benthic
communities, provided that the different nature of underwater sedimentation and biological dispersion processes is accounted for.
Summary
In general, the landform characterization methodology proposed here can serve as a useful mapping and analysis tool
for a variety of resource and environmental studies performed on local or regional scales. The ability to classify the
continuous terrain surface into meaningful and discrete features provides a way to describe, analyze, and quantify the
characteristics of landscape morphology so that they can be
logically related to other aspects of ecosystems. As such, it
can be useful in any analysis and modeling efforts that consider the influence of terrain characteristics on landscape
processes and patterns.
References
Belcher, D.J., 1948. The Engineering Significance of Landforms,
Highway Research Board Bulletin, No. 13.
Beven, K.J., and I.D. Moore, 1993. Terrain Analysis and Distributed
Modelling i n Hydrology, John Wiley & Sons, West Sussex, England, 249 p.
Blaszczynski, Jacek, 1993. HTAS: Hydrologic Terrain Analysis Software User's Manual, Bureau of Land Management, BLM Publication Number BLM/SC/ST-94/007+7000.
Chorley, Richard J., Stanley A. Schumrn, and David E. Sugden, 1985.
Geomorphology, Methuen & Co., New York, N.Y., 605 p.
Jenson, S.K., and J.0. Domingue, 1988. Extracting Topographic
Structure from Digital Elevation Data for Geographic Information
System Analysis, Photogrammetric Engineering b Remote Sensing, 54:1593-1600.
Lueder, D.R., 1959. Aerial Photographic Interpretation Principles and
Application, McGraw-Hill, New York.
Moore, I.D., R.D. Grayson, and A.R. Ladson, 1991. Digital Terrain
Modeling: A Review of Hydrological, Geomorphological and Biological Applications, Hydrological Processes, 5:3-30.
Tanner, W.F., 1974. Advances i n Near-Shore Physical Sedimentology: A Selective Review, Shore and Beach 42.
Zeverbergen, L.W., and C.R. Thorne, 1987. Quantitative Analysis of
Land Surface Topography, Earth Surface Processes and Landforms, 12:47-56.
(Received 8 June 1995; accepted 16 November 1995; revised 17 April
1996)
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